Problem: Simplify the following expression: $x = \dfrac{72q}{36q - 12}$ You can assume $q \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $72q = (2\cdot2\cdot2\cdot3\cdot3 \cdot q)$ The denominator can be factored: $36q - 12 = (2\cdot2\cdot3\cdot3 \cdot q) - (2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $x = \dfrac{(12)(6q)}{(12)(3q - 1)}$ Dividing both the numerator and denominator by $12$ gives: $x = \dfrac{6q}{3q - 1}$